Urban Transportation Planning�Module 7: Traffic Assignment Techniques1

Traffic Assignment – Analytical Methods

1. Urban Transportation Planning Module 7: Traffic Assignment Techniques (Diversion Curves; Basic Elements of Transport Networks, Coding, Route Properties, Path Building Criteria, Skimming Tree, All-or-Nothing Assignment, Capacity Restraint Techniques, Reallocation of Assigned Volumes, Equilibrium Assignment, Multipath Assignment Technique) CSRK Prasad

2. R.R.L. (Moore’s) Algorithm Operates by starting from the origin node, adding all links connected to that origin to the tree and finding the node nearest the origin. Then it branches from that node and determines from these branches, and the remaining branches from the origin node that have not been already used, which is the next nearest node to the origin and so on. These nodes are checked to ensure that they are not already on the tree and the tree building continues or several branches at the same time.

3. 1. Link Table I N J T Link I – Link reference number, indicating serial number N – Origin node of the links numbered in sequential order J – Destination node of the link T Link – Time / Cost along the link

4. 2. Cumulative Table N CUM TCUM Order of Removal NCUM – refers back to the I column in the link table TCUM – cumulative time from the origin to the J node of the link referenced in the NCUM column

5. 3. Tree Table NODE NN TSUM NODE – Node in the network NN – Link by which that node is reached (referencing back NCUM & I in tables II & I TSUM – Minimum time taken to reach that node from the origin node

6. Example Road Network 1 2 3 4 5 7 6 4 3 4 5 6 7 4 4 3 4 8 9 3 4 5 6 7 6 5

7. Link Table I N J T Link 1 1 2 4 2 1 3 3 3 2 1 4 4 2 3 5 5 2 4 4 6 2 5 6 7 3 1 3 8 3 2 4 9 3 5 6 10 3 6 8 11 4 2 4 12 4 5 3 13 4 7 4 14 5 2 7 15 5 3 7 16 5 4 4 17 5 6 3 18 6 3 9 19 6 5 4 20 6 7 5 21 7 4 4 22 7 5 5 23 7 6 5

8. Procedure Step 1: All the values of TSUM are set to a value of 9999 in order to provide a check as to whether a minimum path to the node as already reached or not Step 2: The NN and TSUM for the origin node 1 is set to zero

9. 3. Tree Table NODE NN TSUM 1 2 9999 3 9999 4 9999 5 9999 6 9999 7 9999

10. Procedure Step 3: Starting from origin node 1, all the links connected to it are found out from Link Table and entered them in Cumulative Table. Step 4: The minimum TCUM value amongst the values entered in the Cumulative Table is selected and entered in Tree Table with Node = J, and NN= NCUM by replacing TSUM=9999 by TCUM

11. 2. Cumulative Table N CUM TCUM Order of Removal 1 (1-2) 4 2 (1-3) 3 1

12. 3. Tree Table NODE NN TSUM 1 2 9999 3 2 (1-3) 3 4 9999 5 9999 6 9999 7 9999

13. Procedure Step 5: Returning back to Link Table, all the links that are connected to the last entry in the node column, i.e. 3, are determined. (3-1, 3-2, 3-5 & 3-6) Step 6: A check is now made, for the J nodes of these links that no entry exists in the Tree Table, i.e. TSUM column has not been altered.

14. Link Table I N J T Link 1 1 2 4 2 1 3 3 3 2 1 4 4 2 3 5 5 2 4 4 6 2 5 6 7 3 1 3 8 3 2 4 9 3 5 6 10 3 6 8 11 4 2 4 12 4 5 3 13 4 7 4 14 5 2 7 15 5 3 7 16 5 4 4 17 5 6 3 18 6 3 9 19 6 5 4 20 6 7 5 21 7 4 4 22 7 5 5 23 7 6 5

15. 2. Cumulative Table N CUM TCUM Order of Removal 1 (1-2) 4 2 (1-3) 3 1 7 (3-1) 3+3=6 8 (3-2) 4+3=7 9 (3-5) 6+3=9 10 (3-6) 8+3=11

16. Procedure Step 7: The minimum of all TCUM values excepting that has been removed in order of removal column of Cumulative Table is found out. Step 8: Referencing back to Link Table, the Jth node for the link whose I value is equal to NCUM is found. The N value for this J node is entered in Tree Table in NN column against Node = J. Put 2 in the order of removal column against NCUM=1. Then, repeat the procedure from Step 5 onwards. If at any stage, all the values of TSUM are found to be less than 9999, the tree is terminated.

17. 2. Cumulative Table N CUM TCUM Order of Removal 1 (1-2) 4 2 2 (1-3) 3 1 7 (3-1) 3+3=6 8 (3-2) 4+3=7 9 (3-5) 6+3=9 10 (3-6) 8+3=11

18. 3. Tree Table NODE NN TSUM 1 2 1 (1-2) 4 3 2 (1-3) 3 4 9999 5 9999 6 9999 7 9999

19. Link Table I N J T Link 1 1 2 4 2 1 3 3 3 2 1 4 4 2 3 5 5 2 4 4 6 2 5 6 7 3 1 3 8 3 2 4 9 3 5 6 10 3 6 8 11 4 2 4 12 4 5 3 13 4 7 4 14 5 2 7 15 5 3 7 16 5 4 4 17 5 6 3 18 6 3 9 19 6 5 4 20 6 7 5 21 7 4 4 22 7 5 5 23 7 6 5

20. 2. Cumulative Table N CUM TCUM Order of Removal 1 (1-2) 4 2 2 (1-3) 3 1 7 (3-1) 3+3=6 - 8 (3-2) 3+4=7 - 9 (3-5) 3+6=9 10 (3-6) 3+9=11 3 (2-1) 4+4=8 - 4 (2-3) 4+5=9 - 5 (2-4) 4+4=8 3 6 (2-5) 4+6=10

21. 3. Tree Table NODE NN TSUM 1 2 1 (1-2) 4 3 2 (1-3) 3 4 5 (2-4) 8 5 9999 6 9999 7 9999

22. Link Table I N J T Link 1 1 2 4 2 1 3 3 3 2 1 4 4 2 3 5 5 2 4 4 6 2 5 6 7 3 1 3 8 3 2 4 9 3 5 6 10 3 6 8 11 4 2 4 12 4 5 3 13 4 7 4 14 5 2 7 15 5 3 7 16 5 4 4 17 5 6 3 18 6 3 9 19 6 5 4 20 6 7 5 21 7 4 4 22 7 5 5 23 7 6 5

23. 2. Cumulative Table N CUM TCUM Order of Removal 1 (1-2) 4 2 2 (1-3) 3 1 7 (3-1) 3+3=6 - 8 (3-2) 3+4=7 - 9 (3-5) 3+6=9 4 10 (3-6) 3+9=11 3 (2-1) 4+4=8 - 4 (2-3) 4+5=9 - 5 (2-4) 4+4=8 3 6 (2-5) 4+6=10 11 (4-2) 8+4=12 - 12 (4-5) 8+3=11 13 (4-7) 8+4=12

24. 3. Tree Table NODE NN TSUM 1 2 1 (1-2) 4 3 2 (1-3) 3 4 5 (2-4) 8 5 9 (3-5) 9 6 9999 7 9999

25. Link Table I N J T Link 1 1 2 4 2 1 3 3 3 2 1 4 4 2 3 5 5 2 4 4 6 2 5 6 7 3 1 3 8 3 2 4 9 3 5 6 10 3 6 8 11 4 2 4 12 4 5 3 13 4 7 4 14 5 2 7 15 5 3 7 16 5 4 4 17 5 6 3 18 6 3 9 19 6 5 4 20 6 7 5 21 7 4 4 22 7 5 5 23 7 6 5

26. 2. Cumulative Table N CUM TCUM Order of Removal 1 (1-2) 4 2 2 (1-3) 3 1 7 (3-1) 3+3=6 - 8 (3-2) 3+4=7 - 9 (3-5) 3+6=9 4 10 (3-6) 3+9=11 5 3 (2-1) 4+4=8 - 4 (2-3) 4+5=9 - 5 (2-4) 4+4=8 3 6 (2-5) 4+6=10 - 11 (4-2) 8+4=12 - 12 (4-5) 8+3=11 - 13 (4-7) 8+4=12 14 (5-2) 9+7=16 - 15 (5-3) 9+7=16 - 16 (5-4) 9+4=13 - 17 (5-6) 9+3=12

27. 3. Tree Table NODE NN TSUM 1 2 1 (1-2) 4 3 2 (1-3) 3 4 5 (2-4) 8 5 9 (3-5) 9 6 11 (3-6) 11 7 9999

28. Link Table I N J T Link 1 1 2 4 2 1 3 3 3 2 1 4 4 2 3 5 5 2 4 4 6 2 5 6 7 3 1 3 8 3 2 4 9 3 5 6 10 3 6 8 11 4 2 4 12 4 5 3 13 4 7 4 14 5 2 7 15 5 3 7 16 5 4 4 17 5 6 3 18 6 3 9 19 6 5 4 20 6 7 5 21 7 4 4 22 7 5 5 23 7 6 5

29. 2. Cumulative Table N CUM TCUM Order of Removal 1 (1-2) 4 2 2 (1-3) 3 1 7 (3-1) 3+3=6 - 8 (3-2) 3+4=7 - 9 (3-5) 3+6=9 4 10 (3-6) 3+9=11 5 3 (2-1) 4+4=8 - 4 (2-3) 4+5=9 - 5 (2-4) 4+4=8 3 6 (2-5) 4+6=10 - 11 (4-2) 8+4=12 - 12 (4-5) 8+3=11 - 13 (4-7) 8+4=12 6 14 (5-2) 9+7=16 - 15 (5-3) 9+7=16 - 16 (5-4) 9+4=13 - 17 (5-6) 9+3=12 18 (6-3) 11+9=20 - 19 (6-5) 11+4=15 - 20 (6-7) 11+5=16

30. 3. Tree Table NODE NN TSUM 1 2 1 (1-2) 4 3 2 (1-3) 3 4 5 (2-4) 8 5 9 (3-5) 9 6 11 (3-6) 11 7 13 (4-7) 12

31. Procedure Step 9: Skimming the tree – to determine the actual route through which the minimum path is established, the tree table provides all the information about the network.

32. Shortest Paths 1-2 1-3 1-2-4 1-3-5 1-3-6 1-2-4-7

33. Example Road Network (Shortest Paths) 1 2 3 4 5 7 6 4 3 4 5 6 7 4 4 3 4 8 9 3 4 5 6 7 6 5

34. Example Road Network (Skim Tree) 1 2 3 4 5 7 6 4 3 9 8 12 11

35. Readings Bruton, M. J., An Introduction to Transportation Planning (The Living Environment), UCL Press, London, UK, 2000. Hutchinson, B.G., Principles of Urban Transport Systems Planning, McGraw Hill, 1974. 8/1/2019 CSRK Prasad NIT Warangal 35

36. Contact: [email protected] [email protected] 0870-2462117 (O) 9440347348 (M) 2019-08-01 36 CSRK Prasad